We analyze a secure dual-hop mixed radio frequency-free space optical (RF-FSO) downlink simultaneous wireless information and power transfer (SWIPT) systems. The FSO link and all RF links experience Gamma-Gamma, independent and identical Nakagami-$m$ fading, respectively. We analyze the effects of atmospheric turbulence, pointing error, detection technology, path loss, and energy harvesting on secrecy performance. Signal-to-noise ratios at both legitimate and illegitimate receivers are not independent since they are both simultaneously influenced by the FSO link. We derive the closed-form expression of the secrecy outage probability (SOP) as well as the asymptotic result for SOP when signal-to-noise ratios at relay and legitimate destinations tend to infinity. Monte-Carlo simulations are performed to verify the accuracy of our analysis. The results show that the secrecy diversity order (SDO) depends on the fading parameter of the relay-destination link and the number of the destination's antennas. Additionally, the SDO also depends on the fading parameters, the pointing error parameter, and the detection type of the FSO link.